Conventionally, acrylonitrile-containing fibers commonly have been dyed by a dyeing method using a cationic dye. However, when a cationic dye is used to dye acrylonitrile-containing fibers, a vivid hue can be obtained; however, cationic dyes generally have poor light fastness. Furthermore, in dyeing a fiber product composed of acrylonitrile-containing fibers and polyester-based fibers, a technique is used in which a cationic dye and a disperse dye are placed in the same bath and the acrylonitrile-containing fibers are dyed with the cationic dye while the polyester-based fibers are dyed with the disperse dye. However, when the polyester-based fibers are polyethylene terephthalate fibers (PET fibers), they are usually dyed at a high temperature of 130° C. under high pressure, and thus, in such dyeing conditions, the acrylonitrile-containing fibers that have a glass transition temperature of less than 130° C. are deteriorated in physical properties such as texture and fiber strength. On the other hand, when they are dyed at a temperature at which the physical properties of the acrylonitrile-containing fibers do not deteriorate, the PET fibers cannot be dyed in deep colors. Non-Patent Document 1 proposes carrier dyeing as a method for dyeing PET fibers at normal pressure and a temperature of less than 100° C. Furthermore, as a method for dyeing a fiber product composed of acrylonitrile-containing fibers and polyester-based fibers, a thermosol dyeing method is known in which a fiber product is immersed in a disperse dye solution to be dyed, and thereafter the dye that dyed the fiber product is heated at a temperature of about 190° C. to 220° C. to be fixed to the fibers.
In addition, as a method for dyeing a fiber product, Patent Document 1 proposes a method including applying a water absorbent resin to the surface of a fabric to dye the fiber product with a dye by an inkjet method. On the other hand, with respect to the water absorbent resin, it is known to exhibit various functions not only by being applied to the surface of a fabric but also by being added to fibers. For example, Patent Document 2 describes that a water absorbent resin is added to a polyolefin-based resin such as polypropylene and then this is extruded to obtain reinforcing fibers having good dispersibility in cement. Also with respect to the acrylonitrile-containing fibers, Patent Document 3 describes that a water absorbent resin is dispersed in an acrylonitrile-containing resin and then this is heat-moisture treated to obtain porous fibers.